There is still much we do not know about this virus.
"There is no evidence that" does not = "It will never happen".
Abandoning pets is cruel and irresponsible. Obviously.
However people with pets should be taking proper precautions to protect themselves and others.
With dogs these are the same precautions that they should always take regardless. Exercise good hygiene protocols. Do not let your pet "kiss you" on the face. Pick up your dog's mess immediately and dispose of it hygienically, then wash your hands or use sanitiser. Do not allow your dog to run up to other people and jump up at them. If you are unable to control your dog from doing this keep them on a lead. Wash your hands after touching your pet, especially prior to preparing food.
Felines are sensitive to all kinds of pathogens and viruses that dogs are not vulneable to.
Felines also interact with a diverse range of other species including birds and rodents.
Felines carry their own viruses including feline immune deficiency virus and feline corona virus.
I would suggest that the most significant concern re felines is not cat to human transmission (unlikely but we cannot say it will never happen), it is the possibility of further zoonotic mutation of the virus should a perfect storm of unlikely factors arise.
It seems likely that this virus originated in a wet market in China where multiple diverse species of animals, birds, amphibians, reptiles and even (if reports are true) marsupials were all crowded together in unsanitary conditions.
The virus arose because of different species carrying different viruses had close contact, their blood, urine, faeces, and other body fluids mingled, they breathed on each other and this is how extremely dangerous viruses arise.
One animal, say a bat, carries a virus, it is eaten by a snake, or its blood or urine contaimates an armadillo in the cage beow and bingo. Both animals carry a virus, the RNA of the viruses mutate and evolve and a novel virus is here. If the virus mutates to infect humans then we are in serious trouble.
Ebola and HIV started in this way, as did Sars, Mers and the 1918 so called "Spanish Flu".
This does happen from time to time in nature, however wet markets, the bushmeat trade and international travel mean that a previously dangerous virus that might run out of hosts in the old days can now become a global pandemic.
This virus is zoonotic. It arose from animals. While panic is always unhelpful people should exerise caution and good hygiene protocols around their pets.